Production plan creation system, method, and program

ABSTRACT

The present invention is to formulate a production plan  5  by means of an event-based simulator  4  simulating movement of products within a factory through use of a production process model  2  and a production rule  3.  There are provided a time-interval-based simulator  6  for computing the statuses of production processes at given time intervals, and a rule generator  7  for automatically deriving the production rule  3  through use of the time-interval-based simulator  6.  As a result of a production plan being repeatedly formulated at high speed through use of the time-interval-based simulator  6,  the rule generator  7  can automatically, efficiently formulate the production rule  3  by application of machine learning based on a consecutive optimization method. An event-based simulator  4  devises a high-quality production plan  5  using the generated production rule  3.

FIELD OF THE INVENTION

The present invention relates to a computing system which automaticallycreates a production plan in a factory or the like, as well as to asystem, method, and program for creating a production plan having thefunction of automatically formulating, not by manpower but by acomputing machine, an appropriate production rule required at the timeof devising of a high-quality plan.

BACKGROUND ART

A plurality of production planning systems which support or automatedevising of a production plan in a factory or the like have beenproposed. Many of the production planning systems have already beencommercialized domestically and overseas. Moreover, many manufacturingcompanies have developed proprietary systems and put them into use.

Many of the conventional production planning systems adopt an approachof finding a general solution by formulating a model by means ofsimplifying restrictions on a production process; that is, assuming thatinstallation capacity is infinite, and by applying a mathematicaloptimizing technique, such as a linear planning technique, to thethus-simplified model.

Processes for manufacturing a high-technology part typified by asemiconductor or liquid crystal are formed by repetition of a greatnumber of processes. Those processes are much larger in scale and morecomplicated than processes for manufacturing other products, such asautomobiles. In normal times, the number of processes reaches hundreds,and a manufacturing lead time extends to several months (see, e.g.,Non-Patent Document 1). Moreover, in the field of the high-technologypart industry, new manufacturing processes are developed one afteranother with a view toward improving the competitiveness of products.Since the most advanced manufacturing processes are immediately appliedto production of actual products, the manufacturing processes rarely runstably on a production site. On the occasion of devising a plan tomanufacture high-technology parts, consideration must always be given tovariable factors in manufacturing operation, such as occurrence of afailure in a manufacturing machine or a material defect in products.

Therefore, manufacture of products, such as high-technology products,involving many variable factors in manufacturing processes does notpurport to eliminate work in process (WIP), which is seen in the KANBANscheme considered to be effective in the automobile industry, which ischaracterized by mature manufacturing processes. It is important to seta minimum optimal quantity of inventory which enables stable productionof products without being greatly affected by a change in manufacturingcapability stemming from a mechanical failure or scrapping or reworkingstemming from a material defect. In order to keep needless stock low,highly-accurate demand forecasting is required as a precondition.Highly-accurate demand forecasting is currently taken as an importantproblem in SCM of the high-technology industry. In the semiconductorindustry in the U.S., forecasting a demand for about a year with anerror of 22% or less is taken as an immediate desired target (see, e.g.,Non-Patent Document 6).

On the occasion of implementation of a plan for manufacturinghigh-technology parts, manufacturing processes are of large scale andcomplicated. Hence, optimization using a mathematical method encountersdifficulty in terms of calculation time. For example, in relation tomanufacture of a semiconductor wafer, effectiveness of various job inputrules or dispatching rules has hitherto been verified by means ofscheduling based on a simulation method (see, e.g., Non-Patent Documents5, 7).

In recent years, in contrast with a precise model of actual productionprocesses, faithful simulation of a shift in the quantity of WIP (achange in statuses of respective parts; for example, a change in statusis computed for each process every time processing is completed) becomespossible on a per-event basis, in association with an improvement incomputing speed and a drop in the cost of a calculating machine. Anapproach to selecting the best production plan by repeating simulationbased on a plurality of simple production rules by trial and error hasbecome mainstream, particularly in very complicated production processessuch as manufacture of a semiconductor. However, simulation oflarge-scale and complicated production processes is still verytime-consuming. Therefore, finding a production rule suitable fordevising a high-quality production plan by trial and error is difficult.The conventional production planning system is not provided with asupport function for finding the most important and difficult productionrule. For this reason, there is no way but to relay solely on the skilland guesswork of a production planning worker in devising a high-qualityproduction plan.

There is an example study case where an attempt is made to automaticallygenerate an appropriate rule with a calculating machine by developmentof an artificial intelligence (AI) technique and where the rule isapplied to the production plan problem (e.g., “Learning schedulingcontrol knowledge through reinforcement” Miyashita, K., Internationaltransactions in operational research, Vol. 7, No. 2, pp. 125 to 138,2000, “Job-Shop Scheduling with Genetic Programming” Miyashita, K.,Proc. of the Genetic and Evolutionary Computation Conference, pp. 505 to512, 2000, “Two-stage Learning Method for dynamic job shopscheduling—robust scheduling using a hierarchical neural network” andEguchi et al., Scheduling Symposium, pp. 89 to 94, 2001). However,application of these techniques to a production plan problem intendedfor actual large-scale production processes is difficult to realize, inview of the time required to learn rules. A practical production plansystem having the function of automatically generating appropriateproduction rules still does not exist.

Scheduling based on the conventional simulation scheme has the followingdrawbacks (see Non-Patent Document 8).

When an appropriate product mix or an input rate is determined,performing sufficient examination by trial and error in consideration ofvariations in actual manufacturing processes is still verytime-consuming.

The work determined by simulation is easy to dissociate from actualmanufacturing conditions for reasons of various variable factors in anactual production site, and an effective work instruction to addresssuch a situation cannot be carried out smoothly.

In order to counter the problems, a more high-speed, robust, andproduction-instructive simulation technique is required to devise a planfor producing high-technology parts.

∂Non-Patent Document 1]

Linda F Atherton and Robert W. Atherton. Wafer fabrication; Factoryperformance and Analysis. Kluwer Academic Publishers, 1995.

[Non-Patent Document 2]

L. Gong and H. Matuo. Control Policy for manufacturing system withrandom yield and rework. Journal of Optimization Theory andApplications, 95(1): 149-175, 1997.

Non-Patent Document 3]

Wallace J. Hopp and Mark L. Spearman. FACTORY PHYSICS. McGraw-Hill,second edition, 2000.

Non-Patent Document 4]

J. D. C. Little. Proof of the queueing formula L=λW. OperationsResearch, 9:383387, 1961.

[Non-Patent Document 5]

Oliver Rose. The shortest processing time first (SPTF) dispatching ruleand some variants in semiconductor manufacturing. In Proceeding of the2001 Winter Simulation Conference, pages 1220-1224. INFORMS, 2001.

[Non-Patent Document 6]

Robin Roundy. Report on practices related to demand forecasting forsemiconductor products. Technical report, School of Operations Researchand Industrial Engineering, Cornell University, 2001.

[Non-Patent Document 7]

Lawrence M. Wein. Scheduling semiconductor wafer fabrication. IEEEtransaction on Semiconductor Manufacturing, 1(3): 115-130.1988.

[Non-Patent Document 8]

Masahiro Arakawa, Masahiko Fuyuki, Ichiro Inoue. Examination ofoptimization-oriented simulation base scheduling method in APS, LecturePaper Collection of Scheduling Symposium 2001, pp. 47 to 52, SchedulingSociety, 2001

[Non-Patent Document 9]

Hiroyuki Kashiwase. Method for scheduling production of semiconductorand high-speed simulation model, Master's thesis, Tsukuba University,2002.

DISCLOSURE OF THE INVENTION

According to the conventional production planning technique, anappropriate production rule to be used for devising a high-qualityproduction plan must be provided in advance by a human. However, it isdifficult to formulate a production plan rule appropriate forlarge-scale, complicated production processes with manpower.

Even when a learning method for a conventional artificial intelligencetechnique is merely applied to the technique, automatic generation ofrules for large-scale, complicated production processes, such as thosefor semiconductor production, is very time-consuming, and henceimpractical.

The major object of the present invention is to significantly improvethe efficiency of production of products, such as semiconductors,involving large-scale, complicated production processes.

A lower-priority object of the present invention is to significantlyimprove the efficiency of production of products, such assemiconductors, involving large-scale, complicated production processes,by realizing a production planning system having the function forautomatically generating production rules, which enables devising of ahigh-quality production plan at high speed.

Another lower-priority object of the present invention is tosignificantly improve the efficiency of production of products, bycontrolling production processes such that the quantity of work inprocess falls within a predetermined range.

A system, method, and program of the present invention for formulating aproduction plan are to devise a production plan by simulating movementof products within a factory by an event-based simulator through use ofa production process model and a production rule. The system, method,and program have a time-interval-based simulator for computing thestatuses of production processes at uniform time intervals, and a rulegenerator for automatically deriving the production rule through use ofthe time-interval-based simulator. The production plan is repeatedlydevised over and over again at high speed through use of thetime-interval-based simulator, thereby applying mechanical learningbased on a consecutive optimization method to the rule generator, tothus formulate the rule. Thereby, the production rule can be formulatedautomatically and efficiently. The event-based simulator formulates ahigh-quality production plan through use of the thus-generatedproduction rule.

The present invention is characterized by comprising a simulator forrepeatedly computing the quantity of WIP in manufacturing processes; anda control system which determines a parameter used for computation ofthe simulator such that a computation result of the simulator becomesequal to an allowable range or less and which performs productioncontrol of the production process on the basis of the parameter.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram showing an embodiment of a production planningsystem according to the present invention;

FIG. 2 is a flowchart showing the outline of processing of atime-interval-based simulator;

FIG. 3 is a view showing details of specific information about aproduct, processes, and machinery included in a production process modeland a production plan;

FIG. 4 is a view showing performance of a time-interval-based simulatorplotted on a time axis;

FIG. 5 is a flowchart showing the outline of production status updateprocessing;

FIG. 6 is a view showing an example learning model of a part input ruleusing a neural network;

FIG. 7 is a view showing a cyclic shift in WIP in processes;

FIG. 8 is a view showing a shift in WIP in terms of Periods;

FIG. 9 is a block diagram showing a system configuration according to asecond embodiment; and

FIG. 10 is a flowchart showing processing procedures of a productionsystem.

BEST MODE FOR IMPLEMENTING THE INVENTION First Embodiment

Preferred embodiments of the present invention will now be describedhereinbelow by reference to the drawings. FIG. 1 is a block diagramshowing an embodiment of a production planning system according to thepresent invention. A production process model 2 represents, as a modelin a computer, information pertaining to manufacturing operation in afactory where products are manufactured. Information represented as amodel includes information about manufacturing equipment (e.g., the typeof equipment, the number of pieces of equipment, the capacity of thepieces of equipment, failure rates of the pieces of equipment, or thelike); information about workers engaged in production (a shift,capabilities of the workers, the number of workers, or the like);information about a method for manufacturing products (e.g., machineryto be used, workers, a processing time, a transport time, anon-defective rate, a reworking rate, or the like); information aboutproducts (e.g., the quantity of production, an input time, a due date,or the like), etc. A detailed model pertaining to an actual factory isprepared in the computer on the basis of the foregoing informationitems, and movement of products in the factory is simulated using themodel. From the result of simulation, a production plan draftsmanacquires information about the time by which input products are finishedand the quantity of work in process which will arise in each machine,thereby formulating a desirable production plan 5.

A block 1 shown in FIG. 1 represents the entire production planningsystem. The production process model 2 is a static model of a factoryrepresenting the performance of machinery installed in the factory, thenumber of machines, processes for products to be produced in thefactory, and a quantity of products. The manner in which materialsactually flow within the factory and in which the materials aredynamically changed to products cannot be simulated by only suchinformation. The dynamic aspect of the factory to be embodied as a modelis a set of production rules 3. The main production rules 3 required bythe production planning system 1 are roughly divided into two types ofrules.

One type of rule is a part input rule for determining a timing at whichmaterials of products are to be input. This type of rule encompasses,e.g., a rule for inputting a given quantity of material at a giveninterval and a rule for newly inputting the quantity of materialcorresponding to the quantity of products shipped. Another importanttype of production rule 3 is called a dispatching rule. This dispatchingrule is for determining which of parts is input when the productionmachine of the factory has become able to perform machining undercircumstances where a plurality of parts await machining in a buffer infront of the production machine. Many rules, such as a (First In Firstout) rule for prioritizing a part having first entered a buffer and an(Earliest Due Date) rule for prioritizing parts for products whose duedates will be earliest have already been proposed [R. W. Conway et al.,“Theory of Scheduling,” Addison-Wesley (1986)]. The production rules 3control all of the dynamic aspects of the factory, and hence the stateof production in the factory greatly changes according to the nature ofthe production rules 3 used. Therefore, the most important duty of aproduction administrator of the factory is to determine the nature ofthe production rules 3 which would realize efficient production whenapplied to the production process model 2 of the factory of object. Therelated-art production planning system 1 is based on premise that aproduction plan draftsman inputs the production rules 3. In contrast,the function for supporting the user is embodied by only preparing aplurality of general rules in advance in a selectable manner.

When the production process model 2 and the production rules 3 aredefined, production processes in the actual factory can be simulatedusing information about the model and the rules. An event-basedsimulator 4 runs this simulation. The event-based simulator 4consecutively advances an internal clock and simulates a dynamic changein the production processes by application of the production rules 3 inaccordance with a change (also called an “event”) having arisen at thattiming. For instance, when machining by one machine in the productionprocess model 2 finishes at a certain time (i.e., a value determined byadding a machining time to a machining start time coincides with acurrent time with regard to a part currently being processed by thatmachine in the event-based simulator 4), apart to be machined next isselected from the parts awaiting machining in the buffer of the machinethrough use of the dispatching rule(s) of the production rules 3. Ifrequired conditions, such as an operator and a material, are satisfied,processing is commenced. The event-based simulator 4 advances theinternal clock by performing the foregoing operation from the simulationstart time to the simulation end time, thereby reproducing all changeswhich would be expected to arise within the period of time in thefactory, and outputs the result of reproduction as a production plan 5.Information that the nature of parts and quantities of the parts will bemachined by the respective machines in the factory is recorded along atime axis on the production plan 5. Further, various values pertainingto production, such as an operation rate of facilities, a productionlead time, and a lag behind a due date, are computed on the basis of theinformation, and the computed values are evaluated as the quality of theformulated production plan 5.

The production process model 2, the production rules 3, the event-basedsimulator 4, and the production plan 5, which have been described thusfar, remain unchanged from their counterparts in the related art. Thecharacteristic of the present invention lies in that the productionplanning system 1 is provided with a time-interval-based simulator 6 anda rule generator 7 for automatically generating the production rules 3at high speed. As mentioned previously, the production rules 3 areimportant rules for determining the dynamic characteristic of thefactory, and the quality of the production rules 3 determines thequality of the production plan 5 to be formulated. Therefore,high-speed, automatic generation of the appropriate production rules 3yields an effect of remarkably improving the production efficiency ofthe factory.

The basic principle for generating an appropriate production rule 3using artificial intelligence (AI) technology is consecutiveoptimization [T. Mitchell, “Machine Learning,” McGraw-Hill (1997)].Specifically, processing for formulating the production plan 5 throughuse of a certain set of production rules 3 and improving the productionrule 3 such that the quality of the formulated plan is improved isconsecutively repeated, thereby generating a more pertinent set ofproduction rules 3. Since an actual factory which will be an object ofimplementation of a production plan is of large scale and complicated, amassive amount of computing time is required to repeatedly formulate theproduction plan 5. In the meantime, products generally manufactured inthe factory and facilities used for production are not invariant.Conversely, in the current production environment involving highcompetition and production of small batches of a variety of products,the products and the facilities are usually changed in short cycles.Consequently, even if the production rules 3 can be automaticallygenerated with consumption of an enormous amount of computing time, theproduction process model 2 of the factory may have already been changedwhen the thus-generated production rule is used, and the generatedproduction rules 3 are highly likely to become ineffective. Actualpracticality of the production rules 3 generated by such a technique islow.

Therefore, in order to embody the production rule 1 effective for anactual production site, the production rules 3 must be generated asappropriate at an appropriate timing at which the production rule doesnot become irrelevant to a change in actual production environment. Inorder to automatically, efficiently generate the production rules 3,there is required a simulator capable of repeatedly formulating aproduction plan at high speed over and over again through use of therule generator 7 to which machine learning based on a consecutiveoptimization technique is applied. The simulator is inevitably thetime-interval-based simulator 6 shown in FIG. 1.

FIG. 2 is a flowchart showing the outline of processing of thetime-interval-based simulator 6. The time-interval-based simulator 6formulates the production plan 5 using the data included in theproduction process model 2. First, at the occasion of commencement ofprocessing, the simulator performs setting of required data andinitialization 8. FIG. 3 shows the production process model 2 anddetailed product information12, detailed process information 13, anddetailed machinery information 14, all being included in the productionplan 5. During the data initialization 8, initialization of data to beincluded in the finally-formulated production plan 5 is performed; thatis, initialization of quantity of input, gross production, quantity ofproduction, quantity demanded, quantity of work in process, and anoperation rate, all being shown in FIG. 3. Production plan formulationrequirements described in the production process model 2, such as anorder rate, a process flow, machines used, a processing time, and thenumber of machines, all being shown under given requirements in FIG. 3,are read from the data file, whereupon a time interval at whichsimulation is to be run and an end time are set.

FIG. 4 is a view showing performance of simulation by thetime-interval-based simulator 6 plotted on a time axis. At the time ofperformance of the simulation by the time-interval-based simulator 6,updating of the production status 10 is repeated until the simulationend time comes, in accordance with the time interval set through thedata setting and initialization 8 (step 9). Here, the time intervalspecifies the frequency at which details relating to running ofsimulation are repeatedly updated. No shift is assumed to arise in thequantity of work in process within a predetermined time interval (e.g.,one hour). Performance of simulation means computation of a progress inproduction in each time interval (herein called a time segment 15) byadvancing the internal clock of the simulator on a per-time-intervalbasis. When compared with the volume of computation required by theconventional event-based simulator 4 that frequently updates the statusof a progress in production every time an inventory shift arises withina production process, which is an event, the volume of computation isgreatly diminished by appropriately setting the time interval. As aresult, simulation can be performed efficiently while the accuracy ofsimulation result is maintained.

FIG. 5 is a flowchart showing the outline of processing pertaining toproduction status update 10. When the time-interval-based simulator 6performs processing pertaining to the updating of a production status10, the quantity of parts produced every predetermined time interval iscomputed in connection with all of the machines included in theproduction process (step 16). At this time, of the parts input into themachine until an immediately-before time segment, the quantity of partshaving hitherto finished undergoing processing is computed. Thecapability of the machine assigned to the parts is released, therebyupdating the value of operation rate of the machine (step 17).Subsequently, the quantity of parts to be produced within the set timeinterval is computed in connection with all processes by way of whichthe parts are to be processed by the machine (step 18). At that time,the quantity of production demanded pertaining to a process fallingwithin the current time segment is computed (step 19). If this processis a leading process of products, the quantity demanded is computed bythe part input rule of the production rule 3 described previously. Ifthis process is not the leading process, the quantity demanded is set soas to become equal to the sum of the quantity of products finished in apreceding time segment of a preceding process and the quantity of workremaining in the process in the preceding time segment. Specifically,all of the worked parts originating from the preceding process havingarisen in the preceding time segment are presumed to be shifted to thatprocess and processed in the current time segment. Next, the quantity ofproduction which can be actually realized is computed in connection withthe thus-computed quantity demanded (step 20). At that time, when thedemanded quantity of production determined above includes the quantityof parts produced by the machine capability available in the currenttime district (i.e., the number of machines×operation rate×timeinterval/processing time) and the quantity demanded exceeds the machinecapability, the quantity of inventory to be processed in the next timesegment and subsequent time segments is computed (step 21). Finally, themachine capability [i.e., a time interval/(the number ofmachines×processing time)] to be assigned to production for yielding thethus-computed quantity of production is determined, to thus update theoperation rate of the machine (step 22). The quantity of productionyielded by the machine by way of the overall processes is computed insuccession (step 18). Here, the sequence of processes for assigningparts to the single machine is determined through use of the dispatchingrule of the production rules 3.

As mentioned above, high-speed formulation of a production plan becomesfeasible through use of the time-interval-based simulator 6. Even whenthe time-interval-based simulator 6 is used, the part input rule and thedispatching rule of the production rules 3 are required as describedpreviously. For this reason, there is realized automatic generation ofthe production rules 3 that enables formulation of the production plan 5suitable for the production process model 2, by means of generatingrules using the rule generator 7, and evaluating the quality of theformulated production plan 5 to thus consecutively improve theproduction rules. Proposed as a method for realizing the rule generator7 are various machine learning techniques based on consecutiveoptimization in the field of artificial intelligence, such as NeuralNetwork [C. M. Bishop, “Neural Networks for Pattern Recognition,” OxfordUniversity Press (1995)], Classifier System [P. L. Lanzi et al.,“Learning Classifier System,” Springer (2000)], and Decision TreeLearning [J. R. Quinlan, “C4.5: Programs for Machine Learning,” MorganKaufmann (1993)]. Basically, the rule generator can be realized by useof anyone of the foregoing techniques. Here, an embodiment using aneural network in the rule generator 7 will be described here as anembodiment of the present invention. The concept of the presentinvention is not limited to the embodiment using the neural network andencompasses all machine learning techniques where the rule generator isbased on consecutive optimization.

FIG. 6 shows an example learning model of a part input rule using aneural network as an embodiment. This neural network is disposed foreach machine or each production planning system 1. Used as informationinput to the neural network are information items quantitatively showingthe statuses of production processes and the status of an order, such asthe quantity of inventory, an operation rate of machinery, a back orderwith reference to a due date, and the sum of remaining processingperiods of time required to perform processing pertaining to processesby machines. An output from the neural network corresponds to a partinput rule (any one of four types of rules 00 to 11) to be selected insuch a situation. At the time of learning of the neural network, aweighting value existing between nodes assigned random values isimproved by use of the consecutive optimization technique such aslimited annealing, whereby the part input rule which enables output ofthe high-quality production plan 5 is learned. At this time, the qualityof the production plan 5 created through use of an aggregate ofweighting values of a certain node is evaluated. The weighting valuesare consecutively changed such that the quality of the production plan 5is improved, by means of the influence stemming from a minute change inthe weighting values. Hence, production plan formulation processing mustbe performed an enormous number of times, on the order of thousands oftimes to tens of thousands of times. For this reason, it is difficultfor the related-art event-based simulator 4 to apply the production planformulation processing to formulation of a production plan of a factoryof usual scale, and the time-interval-based simulator 6 of the presentinvention is inevitably employed.

Second Embodiment

In the present embodiment, there is proposed a production scheme forshifting work in processes within only a given time cycle in order torealize stable production in defiance of various fluctuations inmanufacture. The previously-described time-interval-based simulation 6is applied as the simulation technique to the proposed productionscheme. Moreover, it is shown that the time-interval-based simulation 6based on the proposed production scheme enables computation of anequivalent computational result tens of times as fast as does therelated-art simulation technique, through use of data pertaining toactual semiconductor wafer production processes (preceding processes).

CONSTIN” Production Scheme

The present inventor proposes a “CONSTIN” (CONStant Time Interval)production scheme as a production scheme which enables performance ofrobust production, in connection with large-scale, complicatedmanufacturing processes having greatly variable elements. According toCONSTIN, all of the manufacturing processes are exercised synchronously,and work in process shifts from one process to another process withinonly a given cycle (see FIG. 7). Moreover, the extent over which work inprocess shifts during one cycle is one process at the maximum; in otherwords, work in process does not shift beyond the next process.

In CONSTIN, even when fluctuations, such as breakdown of machinery ormaterial defects, have arisen in a certain process, the influence offluctuations can be prevented from spreading across the processes, solong as the fluctuations are solved within the cycle or a sufficientquantity of work in process is planned in a process preceding orsubsequent to the current process. Therefore, the CONSTIN scheme can besaid to be a production scheme which enables performance of robustmanufacturing.

However, CONSTIN improves robustness by limiting free movement of WIP,and valuable production capabilities (resources) cannot be effectivelyutilized without appropriate operation. In the embodiment, simulationshows that such a problem is solved by appropriately setting the valueof the cycle and the quantity of inventory in respective processes.

Model

A model of production processes in the CONSTIN production scheme handledin the present embodiment is described in general terms hereinbelow.Mathematical approximate analysis of this model is provided by Gong etal. (see Non-Patent Publication 2).

In the present embodiment, the model is formulated through use of thefollowing symbols:

m=number of workstations:

g=number of products;

n_(p)=number of processes performed for a product p (where n₀=0);

n=the total number of processes performed for all products;

c=(c₁, c₂, . . . , cm)^(T), production capabilities of workstations inone cycle;

s_(i)=processing time in process i;

S=m×n processing time matrix; the value of an element (k, i) achievedwhen processing pertaining to a process i is performed by a workstationk is s_(j), and 0 in all other cases;

r_(p)(t)=the quantity of input required during cycle t of product p

-   x(t)=x₁x₂(t)₁ . . . , x_(n)(t)^(T); the quantity of production    started in process i(1≦i≦n) during cycle t.-   w(t)=w₁w₂(t)₁ . . . , w_(n)(t)^(T); the quantity of WIP in process    i(1≦i≦n) during cycle t.-   z(t)=z₁z₂(t)₁ . . . , z_(n)(t)^(T); the quantity of production in    process i(1≦i≦n) during cycle t.-   u(t)=u₁u₂(t)₁ . . . , u_(n)(t)^(T); the quantity of rework in    process i(1≦i≦n) during cycle t.-   v(t)=v₁v₂(t)₁ . . . , v_(n)(t)^(T); the quantity of scrap generated    in process i(1≦i≦n) during cycle t.

A shift in WIP during each cycle in the CONSTIN scheme is represented asfollows:

[Mathematical Expression 1]w _(i)(t+1)=w _(i)(t)+r _(p)(t)−(z _(n)(t)−u _(i)(t))In all other cases, the shift is represented as

[Mathematical Expression 2]w _(i)(t+1)=w ₁(t)+(z _(i-1)(t)−u_(i-1)(t)−u_(i-1)(t))−(z _(i)(t)−u_(i)(t)The quantity of production to be started and the quantity of productionin each cycle cannot exceed the quantity of WIP acquired at that pointin time. Hence, the following expression stands. When the lead time inthe process is longer than a set cycle, the quantity of production to bestarted is not always larger than the quantity of production.

[Mathematical Expression 3]x _(i)(t)≦w _(i)(t)

[Mathematical Expression 4]z _(i)(t)≦w _(i)(t)

The production capabilities of the workstations are limited, andproduction in excess of the production capabilities cannot be commenced.Therefore, the following restrictions exist.

[Mathematical Expression 5]Sx(t)≦cSimulation Technique

According to the CONSTIN production scheme, full computation of statuschanges attributable to all events which will arise in productionprocesses, as is done in related-art event-driven simulation, is notperformed. Production processes can be simulated by computing a shift inthe quantity of WIP in respective processes for each cycle. Therefore,in contrast with the related-art simulation technique, a remarkableimprovement in computing speed is expected, and the production scheme isconsidered to be effective as a technique for simulating large-scale,complicated production processes for high-technology parts.

Outline of Simulation Method

Simulation complying with the CONSTIN scheme is performed by exercisinga loop represented by Mathematical Expression 6. [MathematicalExpression 6] initialize Data( ); t = 0; while (t

EndOfSimulation) {  runForPeriod( );  t = t + Period : }

Parameters to be set at that time include a Period constant used fordetermining the cycle of CONSTIN and an EndofSimulation constant usedfor determining a simulation time. A guide employed for determining thePeriod constant will be described later. On the occasion ofdetermination of the latter; that is, the simulation time, only the timerequired to make a simulation result stable must be set. Therefore, asthe value of Period becomes larger, a larger value must be set forEndOfSimulation.

By means of a runForPeriod function which is the core of simulation, ashift in WIP is computed by the respective workstations, as representedby Mathematical Expression 7.

The quantity of WIP at simulation time “t” in a leading process isdetermined by adding to the preliminary quantity of WIP the quantity ofnewly input parts. CONSTIN can realize MRP push-type production orCONWIP (see Non-Patent Document 3) pull-type production by means ofchanging a releaseRule function in Mathematical Expression 7 pertainingto the input rule (Non-Patent Document 9) [Mathematical Expression 7]for (each workstation in the fab) {  for (each step of the workstation){   wip = WIP waiting at step;   if (step is the first process)    wip =wip + releaseRule(step);   demand = wipTranferRule(wip, step); } sortingRule(steps of the workstation);   for(each step in the sortedorder) {   calcProduction (step);   } }A rule to be used fordetermining, of the quantity of WIP in each process, the quantity of WIPto be processed by the workstations in a current cycle corresponds to awipTansferRule function in Mathematical Expression 7. Here, the quantityof shift in WIP in each process must be determined so that productioncan be performed as uniformly as possible, in consideration of thequantity of WIP in processes before and after the current process, thequantity of products having hitherto been finished, and operatingstatues of the workstations in the preceding and subsequent processes.

After the quantity of WIP to be processed in the current cycle among thequantity of WIP in respective cycles has been determined, the processingsequence of processes is determined by a sorting rule function inMathematical Expression 7 on the basis of the priorities of therespective processes determined in the workstation. Processingpertaining to subsequent processes in this sequence cannot be processedin the current cycle, because of limitations on the processingcapabilities of the workstations. A related-art dispatching rule canalso be applied to determination of priorities of the respectiveprocesses. After the quantity of WIP in respective processes to beprocessed by the workstations and the sequence in which the WIP is to beprocessed have been determined, capabilities of the workstations andtime required to perform the processing are computed by a calProductionfunction of Mathematical Expression 7 in accordance with the type ofprocesses (e.g., lot production, batch production, or the like), wherebythe operating statuses of the workstations and the quantity of WIP inrespective processes are updated.

Setting of Cyclic Parameters

When simulation is run in the CONSTIN scheme, an important parameterwhich must be determined in advance is the Period constant. If the valueof Period is made large and simulation is performed until a steady stateis achieved, robustness against variable factors is high. However, manyof pieces of WIP are eventually held in the processes. Conversely, ifthe value of Period is made small, the robustness against the variablefactors becomes low, and computing speed of simulation is alsodecreased. Therefore, an appropriate value of Period must be set inaccordance with the object of simulation. Here, the value of Periodwhich becomes a standard at the time of determination of a value inaccordance with an application can be determined as follows:

Provided that “r” is an input rate, 1_(i) is the number of processes perworkstation, and “d” is the value of Period, the quantity of productionz_(i) of a workstation in one cycle in a steady state is defined asz_(i)=r1_(i)d. In CONSTIN, since the quantity of production is alwayssmaller than the quantity of WIP$\left( {{\sum\limits_{n = 1}^{m}Z_{i}} \leq w} \right),$there stands ${\sum\limits_{n = 1}^{m}{r\quad l_{i}d}} \leq {w.}$

In the meantime, provided that the value of cycle time is taken as “y,”a throughput value is equal to “r” in a steady state. Hence, w=ry isderived from Little's formula pertaining to a queue (Non-Patent Document4). From the foregoing inequality, we have$d \leq {{yl}\quad{\sum\limits_{n = 1}^{m}{l_{i}.}}}$

Although the value of “1” is evident from the model of productionprocesses, a value “y” is usually unknown, because the cycle timeincludes a queuing time in addition to including the time required bythe processes. However, since the cycle time is always larger than theproduction lead time in the processes, there stands${y \geq {\sum\limits_{n = 1}^{m}S_{i}}},$and we have$d \leq {\sum\limits_{n = i}^{m}{S_{i}l\quad{\sum\limits_{f = r}^{m}{l_{j}.}}}}$

From the foregoing description, when there is not information, such as acorrelation between the lead time and the cycle time in actualproduction processes acquired in the past, taking$d = {\alpha\quad{\sum\limits_{i = 1}^{m}{S_{i}l\quad{\sum\limits_{j = 1}^{m}l_{j}}}}}$as a reference value of the Period parameter is appropriate by assuming$y = {\alpha\quad{\sum\limits_{j = 1}^{m}S_{i}}}$(where α˜2).

Application of CONSTIN to Semiconductor Wafer Processing Process

In order to verify the effectiveness of the CONSTIN production schemeand that of a simulation technique based thereon, a numerical experimentis performed through use of data pertaining to semiconductor waferprocessing. The problem used in the experiment is the benchmark problemabout SEMATECH publicly released by the MASM laboratory of Arizona StateUniversity. The problem can be downloaded from URL(http://www.was.asu.edu/¥%7Emasmlab/home.htm) of the MASM laboratory.

An overview of the problem taken in the embodiment is shown in Table 1.For reasons of limitations on modeling of the event-driven simulatorused for the purpose of comparison, minimum changes are made on aportion of the data pertaining to the problem from the viewpoint of thebenchmark problem. TABLE 1 Overview of Test Problem PRODUCT TYPENON-VOLATILE MEMORY NUMBER OF PROCESS  2 FLOWS NUMBER OF TYPES  2 (ONEFLOW FOR EACH TYPE) TYPE OF WORKSTATION  83 NUMBER OF 265 WORKSTATIONSNUMBER OF PROCESSES 210 (PRODUCT A) 245 (PRODUCT B) TOTAL PROCESSINGTIME 313.4 (PRODUCT A) 358.6 (PRODUCT B) QUANTITYE OF DEMANDED 380.95SHEETS/DAY (PRODUCT A) 190.48 SHEETS/DAY (PRODUCT B)

Requirements for Simulation

In the present embodiment, in order to verify the CONSTIN productionscheme and the basic performance of simulation based on the scheme, atest is conducted on the basis of the following assumptions; that is,(1) a processing time of a process is constant; (2) a down time is nottaken into consideration; (3) operators are not taken intoconsideration; and (4) machine failures, discarding, and reworking donot arise. Therefore, the simulation performed in the present embodimentdoes not contain any random elements.

The test performed during this time used the constant input rule basedon the quantity demanded as releaseRule to be used for runningsimulation, a rule for processing all unprocesed WIP as wipTransferRule,and a rule for prioritizing a process having a larger quantity of WIPafter normalization has been performed by the input rate and theprocessing time as sortingRule.

In connection with the Period parameters, a mean total processing timeper wafer achieved in the test is about 8862 minutes, and the meannumber of processes is 221.7.

The value of Period is set to 80 minutes on the premise that α˜2. Thevalue of EndOfSimulation parameter is set to six months so that thesimulation result sufficiently achieves a steady state, and the resultsachieved in the last one month are analyzed and examined.

Simulation Results and Examination thereof

In order to verify effectiveness of the simulation technique proposed inthe embodiment, simulation results are compared with each other throughuse of AutoSched ΛP manufactured by Brooks Autoamtion Co., Ltd. which isa commercially-available event-driven simulator. The result ofcomparison is shown in Table 2. From the comparison result, thesimulation results can be said to be essentially equal to each other,except for WIP. TABLE 2 Comparison between Simulation Results CONSTINAutoSched Quantity of production (product A) 237 239 (product B) 122 120WIP (product A) 157 101 (product B) 85 62 Mean operation rate (%) 37.938.0 Computing time (sec.) 4.5 106

In relation to the quantity of WIP, shifting of WIP is prohibited for agiven period of time in the CONSTIN scheme. Hence, an increase in thequantity of WIP is natural. Presence of such WIP is responsible for animprovement in the robustness of CONSTIN. Therefore, when the value ofPeriod is set, a trade-off between the volume of WIP and the robustnessof production must be taken into consideration.

FIG. 8 shows a change in the quantity of WIP due to a change in thevalue of Period caused by the simulation results. As is evident from thedrawing, the quantity of WIP increases essentially linearly inaccordance with the value of Period.

Provided that the quantity of WIP of the product “p” is taken as Wp,there is obtained $\begin{matrix}\begin{matrix}{{{W_{p}(t)} = {\sum\limits_{n_{p}}^{n_{p}}w}};(t)} \\{= {\sum\limits^{n_{p}}\left( {{w_{i}\left( {t - 1} \right)} +} \right.}} \\{{z_{i - 1}\left( {t - 1} \right)} - {z_{i}\left( {t - 1} \right)}} \\{= {{\sum\limits^{n_{p}}{z_{i - 1}\left( {t - 1} \right)}} +}} \\{\sum\limits^{n_{p}}\left( {{w_{i}\left( {t - 1} \right)} - {z_{i}\left( {t - 1} \right)}} \right)}\end{matrix} & \left\lbrack {{Mathematical}\quad{Expression}\quad 8} \right\rbrack\end{matrix}$

Now, when “t” assumes a sufficiently large value, simulation reaches asteady state. As a result, the quantity of input and the quantity ofproduction become equal to each other, and the quantity of inventorybecomes constant. Therefore, the value of Σ^(n) ^(p) Z_(i1)(t-1)converges at the sum of quantities input in all of the processesacquired during a time Period, and Σ^(n) ^(p) (w_(j-1)(t-1)−z₁(t-1))converges at a comparatively small constant.

For this reason, when the value of Period is large, we have

[Mathematical Expression 9]{overscore (W)}_(p)˜{overscore (r_(p))}n_(p)PeriodThis value coincides closely with the simulation result, as shown inFIG. 8.

In relation to the processing speed, a computing time required to runsimulation for six months using a PC equipped with Pentium (Trademark) 3(1.2 GHz) is merely five seconds in the CONSTIN scheme. The processingspeed is 20 times as fast as the AutoSched, which is thecommercially-available event-driven simulator. When the value of Periodis increased, a computing speed increases essentially linearly inCONSTIN. Therefore, when the value of Period is set to 480 in a footnotetest, the computing time is about one second. Simulation can be appliedto an application requiring a real-time characteristic by means ofappropriately setting the value of Period.

Summary

In the processes for manufacturing semiconductor having many variablefactors, smooth production becomes impossible when the inventory iscurtailed excessively. However, if the inventory is not controlledappropriately, deterioration of a lead time and an increase in thequantity of dead stock will arise. In the CONSTIN scheme described inconnection with the present embodiment, the magnitude of changes inmanufacturing processes is considered to be substituted by the cycle ofmovement of WIP, whereby the appropriate quantity of WIP in respectiveprocesses can be computed. Production in respective processes iscontrolled such that the quantity of WIP is maintained, whereby therobustness of the overall manufacturing processes can be maintained.

Moreover, by means of high-speed simulation based on the CONSTINtechnique, elaborate analysis becomes possible. Setting of anappropriate input rate and a product mix and examination ofcountermeasures against occurrence of mechanical failures which cannotbe solved within the Period can be simulated with high accuracy.

FIG. 9 shows the configuration of the production system for embodyingthe foregoing production method. In FIG. 9, reference numeral 100designates a production facility installed along processes formanufacturing products. Reference numeral 110 designates a controlsystem for controlling manufacturing processes of the productionfacility, and the control system has at least one computer. A controlprogram of the present invention is stored in this control system 110.The essential requirement is to record the control program in arecording medium and install the program from the recording medium intothe control system 110.

Details of processing to be executed by the control system 110 inaccordance with the control program will now be described by referenceto FIG. 10.

The control system 110 repeatedly performs processing procedures shownin FIG. 10 at a given cycle (processing defined by the functionexpressed in Mathematical Expression 6). The control system 110initially sets various parameters showing production statuses of themanufacturing processes of the production facility; for example, thequantity of material input, thereby computing the quantity of WIP inrespective processes within the manufacturing processes by virtue of thefunction expressed in Mathematical Expression 7 (from step S10 to S20).The initial setting values may be input beforehand by way of a keyboardor the like; or various parameters pertaining to production by means ofthe production facility may be measured and the result of measurementautomatically input to the control system 110.

The control system 110 compares the result of computation of thequantity of WIP with a preset tolerance (step S30). When the result ofcomputation of the quantity of WIP falls within the range of tolerance,the production facility 110 is controlled such that the quantity of WIPin actual manufacturing processes becomes equal to the set quantity ofWIP (step S50).

In contrast, when the quantity of a shift in WIP does not fall withinthe range of tolerance, parameters to be used for computation areincremented (increased) or decremented (decreased) by only apredetermined value (step S40).

Specifically, when the quantity of WIP is smaller than the range oftolerance, the parameters are changed to increase the quantity ofmaterial input such that production of products is increased.

Manufacturing processes of the production facility 100 are controlled onthe basis of the parameters (step S50). When the control system 110performs processing pertaining to production control for each cycle(step 50), the quantity of products produced is increased, whilst thequantity of shift in WIP is decreased. As a result, when the quantity ofWIP existing in the respective processes counted through use ofmeasurement equipment (installedin the control system 110 shown inFIG. 1) which measures in real time the production status of a POP(Point of Production) system has become equal to the computation resultof quantity of WIP set in step 20, production in the manufacturingprocesses of the production facility 100 is halted. In the next cycle,production control pertaining to step 50 is again performed, andproduction in the manufacturing processes of the production facility isresumed. By means of performing such a control operation, the controlsystem 110 performs production such that the quantity of WIP ismaintained constant at all times. Such a control operation is repeatedlyperformed at a given cycle. In the simulation for computing the quantityof WIP (the program for simulation performs the function of thesimulator), the function of the time-interval-based simulator and thatof the rule generator, both being described in the first embodiment, areimparted to the control system 110. It is better for the control system110 to repeatedly compute the quantity of WIP in manufacturing processesthrough use of the production rule generated by the rule generator.

DEFINITIONS AND MEANINGS OF TERMS

a. WIP

Materials or works in process which exist in production processes. Thisterm does not include the inventory of finished products.

b. Quantity of Shift in WIP (quantity of shift)

Production proceeds as a result of the WIP “moving” through theprocesses. Therefore, the quantity of shift in WIP signifies thequantity of WIP to be processed through the processes in one cycle.

c. Workstation

Production machines (e.g., a stepper, a dry etching system, or the like)

d. Quantity of Products Input

The quantity of materials input into processes for producing products onthe basis of a plan (based on demand forecasting). The input rate is thequantity of input per unit time. The plan is usually formulated so as tocoincide with a demand rate (the quantity of demand per unit time).

e. Variations in Manufacturing Processes

Primarily variations in operation rate of machine responsible forfailures and variations in manufacturing yield (the ratio ofnon-defective products in the quantity of all products) in the presentpatent application.

f. Movement Cycle

A cycle at which WIP moves

g. Robust

Often translated as “sturdiness” in Japanese. This signifies the abilityto perform production as originally planned even when theabove-described variations have arisen.

h. Trade-Off

A compromise arranged when a plurality of requirements are present.

i. Product Mix

A production proportion when a plurality of products are produced in oneproduction process.

The above-described embodiments are illustrated for comprehension of theinvention described in claims. Therefore, at the time of practice of thepresent invention, various modifications other than the foregoingembodiments are possible. The modifications fall within the technicalscope of the present invention, so long as the modifications are basedon the technical concept of the invention described in the claims.

INDUSTRIAL APPLICABILITY

As has been described above, according to the present invention, anappropriate production rule (a part input rule or the like) can beautomatically generated in connection with production processes whichare objects of a production plan, a product mix, and the quantity ofproduction, through use of a high-speed time-interval-based simulator. Ahigh-quality production plan can be devised in connection withlarge-scale production processes of semiconductors or the like.

Further, according to the present invention, manufacturing processes aresubjected to production control such that the quantity of WIP fallswithin the range of tolerance. Hence, useless WIP (a stock of parts)does not arise during the production processes. Moreover, the productionefficiency is improved significantly.

1. A production plan devising system for formulating a production planby means of simulating movement of a product in a factory by anevent-based simulator through use of a production process model and aproduction rule, the production plan devising system comprising: atime-interval-based simulator for computing the status of a productionprocess at given time intervals; and a rule generator for automaticallyderiving the production rule through use of the time-interval-basedsimulator.
 2. The production plan devising system according to claim 1,wherein the production rule is formulated by means of a machine learningmethod based on a consecutive optimization technique using an artificialintelligence technique.
 3. The production plan devising system accordingto claim 1, wherein the rule generator is constituted by a neuralnetwork.
 4. A production plan devising method for formulating aproduction plan by means of simulating movement of a product in afactory by an event-based simulator through use of a production processmodel and a production rule, the production plan devising methodemploying a time-interval-based simulator for computing the status of aproduction process at given time intervals and a rule generator forautomatically deriving the production rule through use of thetime-interval-based simulator, the production plan devising methodcomprising: a step for repeatedly devising a production plan over andover again by the time-interval-based simulator; a step for applyingmechanical learning based on a consecutive optimization technique to therule generator; a step for automatically formulating the productionrule; a step for using a generated production rule by the event-basedsimulator; and a step for formulating a production rule.
 5. A productionplan devising program for formulating a production plan by means ofsimulating movement of a product in a factory by an event-basedsimulator through use of a production process model and a productionrule, the production plan devising program comprising: atime-interval-based simulator for computing the status of a productionprocess at given time intervals; and a rule generator for automaticallyderiving the production rule through use of the time-interval-basedsimulator, wherein there are performed procedures by means of which thetime-interval-based simulator repeatedly devises a production plan overand over again, thereby applying mechanical learning based on aconsecutive optimization technique to the rule generator, so that theproduction rule is automatically formulated and the event-basedsimulator uses a generated production rule, thereby formulating aproduction rule.
 6. A production system comprising: a simulator forrepeatedly computing the amount of WIP in manufacturing processes; and acontrol system which determines a parameter to be used in computation ofthe simulator such that a computation result of the simulator becomesequal to an allowable range or less, and which controls themanufacturing processes on the basis of the parameter.
 7. The productionsystem according to claim 6, wherein the simulator comprises: atime-interval-based simulator for computing the status of a productionprocess at given time intervals, and a rule generator for automaticallyderiving the production rule through use of the time-interval-basedsimulator, and the simulator repeatedly computes the quantity of WIP inmanufacturing processes through use of a production rule generated bythe generator.
 8. The production system according to claim 6, whereinthe control system has measurement equipment for measuring the amount ofactual WIP in manufacturing processes; and, when the amount of actualWIP measured by the measurement equipment within a given cycle hasbecome equal to a computation result of the simulator, the controlsystem suspends production in manufacturing processes and resumesproduction in the next cycle.
 9. The production system according toclaim 8, wherein the given cycle can be variably set.
 10. A productionmethod comprising: a step for repeatedly computing the amount of WIP inmanufacturing processes by means of a simulator; a step for determininga parameter to be used in computation of the simulator such that acomputation result of the simulator becomes equal to an allowable rangeor less; and a step for controlling the manufacturing processes by acontrol system on the basis of the parameter.
 11. The production methodaccording to claim 10, wherein the simulator comprises: atime-interval-based simulator for computing the status of a productionprocess at given time intervals and a rule generator for automaticallyderiving the production rule through use of the time-interval-basedsimulator, and the simulator repeatedly computes the quantity of WIP inmanufacturing processes through use of a production rule generated bythe generator.
 12. The production method according to claim 10, whereinthe control system has measurement equipment for measuring the amount ofactual WIP in manufacturing processes; and, when the amount of actualWIP measured by the measurement equipment within a given cycle hasbecome equal to a computation result of the simulator, the controlsystem suspends production in manufacturing processes and resumesproduction in the next cycle.
 13. The production method according toclaim 12, wherein the given cycle can be variably set.
 14. A program tobe performed by a production system, the program comprising: a step forrepeatedly computing the amount of WIP in manufacturing processes; astep for determining a parameter to be used in computation of thesimulator such that a computation result of the simulator becomes equalto an allowable range or less; and a step for controlling themanufacturing processes on the basis of the parameter.
 15. The programaccording to claim 14, wherein the production system comprises: atime-interval-based simulator for computing the status of a productionprocess at given time intervals, and a rule generator for automaticallyderiving the production rule through use of the time-interval-basedsimulator, and the simulator performs processing pertaining to a step ofrepeatedly computing the quantity of WIP in manufacturing processesthrough use of a production rule generated by the generator.
 16. Theprogram according to claim 14, wherein the control system hasmeasurement equipment for measuring the amount of actual WIP inmanufacturing processes; and, when the amount of actual WIP measured bythe measurement equipment within a given cycle has become equal to acomputation result of the simulator, the control system suspendsproduction in manufacturing processes and resumes production in the nextcycle.
 17. The production method according to claim 16, wherein thegiven cycle can be variably set.
 18. A recording medium on which theprogram defined in claim 14 is recorded.